CERN-ACC-2015-0212

EuCARD-2Enhanced European Coordination for Accelerator Research & Development

Journal Publication

Experimental investigation of thebehaviour of tungsten and molybdenum

alloys at high strain-rate andtemperature

Scapin, Martina (POLITO) et al

07 September 2015

The EuCARD-2 Enhanced European Coordination for Accelerator Research &Development project is co-funded by the partners and the European Commission under

Capacities 7th Framework Programme, Grant Agreement 312453.

This work is part of EuCARD-2 Work Package 11: Collimator Materials for fast HighDensity Energy Deposition (COMA-HDED).

The electronic version of this EuCARD-2 Publication is available via the EuCARD-2 web site<http://eucard2.web.cern.ch/> or on the CERN Document Server at the following URL:

<http://cds.cern.ch/search?p=CERN-ACC-2015-0212>

CERN-ACC-2015-0212

EPJ Web of Conferences 94, 01021 (2015)DOI: 10.1051/epjconf/20159401021c© Owned by the authors, published by EDP Sciences, 2015

Experimental investigation of the behaviour of tungsten and molybdenumalloys at high strain-rate and temperature

Martina Scapin1,a, Claudio Fichera1, Federico Carra1,2, and Lorenzo Peroni1

1 Politecnico di Torino, Mechanical and Aerospace Engineering Department2 CERN, Engineering Department, Mechanical & Materials Engineering Group

Abstract. The introduction in recent years of new, extremely energetic particle accelerators such as the Large Hadron Collider(LHC) gives impulse to the development and testing of refractory metals and alloys based on molybdenum and tungsten to beused as structural materials. In this perspective, in this work the experimental results of a tests campaign on Inermet R© IT180and pure Molybdenum (sintered by two different producers) are presented. The investigation of the mechanical behaviour wasperformed in tension varying the strain-rates, the temperatures and both of them. Overall six orders of magnitude in strain-rate(between 10−3 and 103 s−1) were covered, starting from quasi-static up to high dynamic loading conditions. The high strain-ratetests were performed using a direct Hopkinson Bar setup. Both in quasi-static and high strain-rate conditions, the heating of thespecimens was obtained with an induction coil system, controlled in feedback loop, based on measurements from thermocouplesdirectly welded on the specimen. The temperature range varied between 25 and 1000 ◦C. The experimental data were, finally,used to extract the parameters of the Zerilli-Armstrong model used to reproduce the mechanical behaviour of the investigatedmaterials.

1. Introduction

The introduction in recent years of new, extremelyenergetic particle accelerators such as the Large HadronCollider (LHC) required the development of advancedmethods to predict the behaviour of components, suchas the Beam Intercepting Devices (BID), in case ofdirect beam impact. For this reasons some componentsof the LHC machine are designed to operate in harshradioactive environment highly solicited from thermo-structural point of view. As a matter of fact, they candirectly interact with high energy beam and, in caseof accident, the energy deposition on the bulk materialcould be potentially destructive. The impact produces asudden energy deposition in the components generatingoutgoing of shock-waves and deforming the material invery high strain-rate and temperature conditions [1,2]. Inorder to study and predict the impact effects, the numericalsimulations of the materials response via FE codes couldbe fundamental [3]. In the same way, they could representthe reference point for the design of complex experimentaltests directly performed in the accelerator [4]. Obviously,reliable predictions need that the materials behaviour isdescribed through confident constitutive relationships.

This context gives impulse to the developmentand testing of refractory metals and alloys based onmolybdenum, tungsten, rhenium and iridium to be used asstructural materials. In the scientific literature, few workscan be found in which the mechanical characterizationof these materials was performed in a wide range oftemperature and strain-rate (e.g. [5–7]). Moreover, not

a Corresponding author: martina.scapin@polito.it

always a strength model calibration was performed, whichotherwise it is fundamental in FE simulations.

In this perspective, in this work the experimentalresults of a testing campaign on Inermet R© IT180 and puremolybdenum are presented. Given the extreme loadingconditions in which the materials could operate (e.g.thermo-mechanical shocks in accident situations), theinvestigation of the mechanical behaviour was performedin a wide range of strain-rates and temperatures. Finally,the experimental data are analyzed and used to extract theparameters of the Zerilli-Armstrong model [8].

2. Materials under investigationThe materials under investigation are a tungsten heavy-alloy and pure molybdenum.

The tungsten alloy is INERMET R© IT180 (IT180 inthe following), supplied by Plansee, which is actually usedin the collimation system of the Large Hadron Collider atCERN. The material has a nominal composition of 95 wt%W, 3.5 wt% Ni and 1.5 wt% Cu. As it is possible to seefrom the microstructure of Fig. 1, the W grains are quitebig, with an average dimension of about 100 µm, andare surrounded by the binder phase. The second phase isa W-Ni-Cu mixture, has a low melting point, representsthe ductile connection between the brittle W grains and,finally, provides the necessary thermal and electricallycontinuity to the material. The material behaviour in termsof flow stress and damage is a consequence of the complexinteraction between the behaviour of the two phases,depending on the values of strain-rate and temperature.The material could show different types of failure modes[7]: tungsten-tungsten grain boundary separation, tungsten

This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution,and reproduction in any medium, provided the original work is properly cited.

Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20159401021

EPJ Web of Conferences

Figure 1. IT180 microstructure.

Figure 2. Pure molybdenum microstructure (Mo1).

grain cleavage, tungsten-binder interfacial separation andmatrix fracture.

In Fig. 2, the microstructure of pure molybdenumis reported. The material is obtained starting from fine-grained metal powders of high purity which are pressed,sintered, hot worked and finally annealed to obtain aregular grain structure.

In more details, two different materials are analyzed,which nominally differ only for the producer: one issupplied by Plansee (in the following Mo1) and the secondone by AT&M (in the following Mo2).

3. Experimental testsThe mechanical characterization was performed both intension and compression, but in this work the attention isfocused on the results obtained in tension. The specimenhas a gage length of 5 mm and a diameter of 3 mm [9].

A series of tests at room temperature at different strain-rates is performed in order to obtain information about thestrain and strain-rate sensitivity of the material. The strain-rate sensitivity is investigated starting from 10−3 s−1 upto 101 s−1. For all the materials, the test at 103 s−1 is notperformed since in this condition the material is too brittleand no reliable results can be obtained. The medium-low strain-rate test are performed using electro-mechanical

and servo-hydraulic testing machines. The high strain-ratecondition is reached by means of a Hopkinson Bar setup indirect configuration.

In addition, a series of tests at different temperatures inboth quasi-static and high strain-rate loading conditions isperformed in order to obtain information about the thermalsoftening of the material. The atmosphere of the tests is air:this is not a problem for IT180, which is not subjected toheavy oxidation, while for molybdenum inert atmosphereshould be used. The temperature range varies between25 ◦C and 800 ◦C in quasi-static loading conditions, whiletemperatures up to 1000 ◦C are investigated at high strain-rate. The difference is mainly due to the fact that at lowstrain-rate the test duration is too high and the testingequipment could not withstand a high temperature for along time; on the other hand, the dynamic test duration isabout 400 µs.

The experimental setups and the testing methodologyare widely described in [9].

For each testing condition at least three repetitions areperformed in order to control the data scattering, then theaverage curves is reported in Figs. 3–5. The results areshown in terms of engineering stress vs. engineering straincurves at different loading conditions.

The evaluation of the data scatter is performedcalculating the mean standard deviation for each loadingcondition, as reported in Table 1. The repeatability of thetests is good for the three materials, even if Mo2 is thematerial with the highest dispersion.

Looking at the results in terms of engineering stressvs. strain, it is possible to conclude that both IT180 alloyand pure molybdenum are temperature and strain-ratesensitive. Moreover the behaviour is such expected forBCC materials: the yield stress is a function of temperatureand strain-rate and this justify the choice of the Z-A model.

Analyzing in more detail the IT180 results, itis possible to notice that the elongation at failuredramatically decreases increasing the strain-rate, whileat high temperature (both in quasi-static and dynamicregimes), it grows increasing the temperature, reachesa maximum and then decreases again for very hightemperature. Moreover, the tests are characterized by theabsence of necking, which allows to analytically analyzethe results. At high strain-rate, a temperature of 200 ◦C isneeded for performing the test.

For what concerns the two grades of pure molyb-denum, it is possible to notice that, in general, boththe materials exhibit some yielding instabilities. The twomaterials have a similar behaviour, even if a higherstability at very high temperature is found for Mo2.Increasing the temperatures (both in quasi-static anddynamic cases), the materials strength decreases, showinga sort of plateau effect starting from 400 ◦C. In thesame manner, also the elongation at failure increases.Increasing the strain-rate the materials harden and reducethe elongation at failure.

At high strain-rate, a temperature of 100 ◦C is sufficientfor performing the test. Starting from medium-high strain-rate (above 101 s−1), over a certain amount of deformation,the plastic work becomes relevant as well as the heatgenerated inside the specimen. In this condition, the

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25°C

200°C

400°C

600°C

800°C

@ 10-3 s-1

a)100°C

@ 103 s-1

200°C

400°C

600°C

800°C

300°C

b)

1000°C

10 s-1

10-3 s-1

@ 25°C

10-1 s-1c)

Figure 3. IT180 – Engineering stress vs. strain curves: a) quasi-static loading condition varying the temperature; b) dynamicloading condition varying the temperature and c) tests at roomtemperature varying the strain-rate.

thermal softening balances and overcomes the effect of thestrain-rate hardening: the deformation process starts to beadiabatic.

4. Data analysisThe experimental results showed that the materials arestrongly dependent on strain, strain-rate and temperature.For these reasons, it is important to find an appropriate

25°C

200°C

400°C

600°C

800°C

@ 10-3 s-1

a)

@ 103 s-1

200°C

400°C600°C

800°C

100°C

300°C

b)

900°C

1000°C

10 s-1

10-3 s-1

@ 25°C

10-1 s-1

c)

Figure 4. Mo1 – Engineering stress vs. strain curves: a) quasi-static loading condition varying the temperature; b) dynamicloading condition varying the temperature and c) tests at roomtemperature varying the strain-rate.

material model for the mechanical behaviour descriptionand a suitable strategy for the parameters identification.

As it is well known, in the scientific literature, it ispossible to find a great number of constitutive modelsfor the viscoplastic flow description. One of the simplestmodels able to take into account a coupling effect betweentemperature and strain-rate and which is suitable for BCCmaterials is the Zerilli-Armstrong model. It expresses theflow stress as a function of the plastic strain, the strain-rate

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25°C

200°C

400°C600°C800°C

@ 10-3 s-1

a)

@ 103 s-1

200°C

400°C600°C

800°C

100°C

300°C

b)

1000°C

10 s-1

10-3 s-1

@ 25°C

10-1 s-1

c)

Figure 5. Mo2 – Engineering stress vs. strain curves: a) quasi-static loading condition varying the temperature; b) dynamicloading condition varying the temperature and c) tests at roomtemperature varying the strain-rate.

and the absolute temperature:

σy = C1 + C2e(−C3+C4 ln ε̇)T + C5εn (1)

in which Ci are the material model parameters. Inaccordance with the original formulation, some of theseparameters could be related to physical quantities of thematerial, but in this work all of them are consideredas optimization variables. In more detail, they areobtained via a multi-objective optimization process, in

Table 1. Data scatter for IT180, Mo1 and Mo2 in terms of meanstandard deviation (MPa).

IT180 Mo1 Mo210−3s−1 @ 25 ◦C 11 7 2510−3s−1 @ 100 ◦C 2 - -10−3s−1 @ 200 ◦C 3 8 2610−3s−1 @ 400 ◦C 12 10 3310−3s−1 @ 600 ◦C 10 9 2410−3s−1 @ 800 ◦C 11 27 810−1s−1 @ 25 ◦C 15 10 28101s−1 @ 25 ◦C 7 22 6103s−1 @ 100 ◦C - 11 7103s−1 @ 200 ◦C 18 11 30103s−1 @ 300 ◦C 14 14 20103s−1 @ 400 ◦C 19 4 31103s−1 @ 600 ◦C 2 7 14103s−1 @ 800 ◦C 10 16 20103s−1 @ 900 ◦C - 36 -103s−1 @ 1000 ◦C 3 25 9

Table 2. Optimized parameters of the Z-A model for the threematerials.

C1

(MPa)C2

(MPa)C3

(10−3/K)C4

(10−4/K)C5

(MPa)n(-)

IT180 21 2572 3.416 1.591 915 0.497Mo1 0 4030 6.449 3.073 524 0.110Mo2 0 2833 5.203 2.639 485 0.135

which at the same time the data coming from differentloading conditions are simultaneously used as targets. Theoptimization is based on the minimisation of the sum ofthe single normalized mean square errors.

Due to the different plastic behaviour of IT180 andmolybdenum, two different approaches are followed.

In case of IT180, an analytical approach is used, inwhich the data fitting is performed on true stress vs. trueplastic strain curves calculated from the engineering ones(under the hypothesis of volume conservation). The rangeof applicability in strain is limited by the instability strain(maximum of the engineering stress vs. strain curves),which is sufficient in case of IT180. A series of differentsolutions are analyzed and good results, in terms ofcorrelation between experimental and predicted responses,are obtained when the experimental data at temperatureover 400 ◦C in quasi-static condition are omitted from theoptimization process. In the optimization all the availablerepetitions are taken into account for the determination of6 unknown (a more in-depth description of the procedure isreported in [9]). The optimized parameters are summarizedin Table 2.

On the other hand, in case of Mo1 and Mo2, anumerical inverse approach is used. The parametersidentification is reached varying the material strengthparameters of the FE models (one for each experimentalloading and constraint condition) and comparing themodel results with the experimental data with the aim toobtain the best correlation. The great advantage of thisprocedure is that no hypothesis about the internal specimenstress-strain, temperature or strain-rate fields is made: infact, the comparison is made in terms of macroscopic

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Table 3. Percentage Normalized Mean Square Error for IT180,Mo1 and Mo2 obtained by the comparison between target andcomputed curves (“nc” means that data of the correspondingloading conditions is not considered in the optimization).

IT180 Mo1 Mo210−3s−1 @ 25 ◦C 0.0342 0.0492 0.058210−3s−1 @ 100 ◦C 0.0339 - -10−3s−1 @ 200 ◦C 0.0424 nc nc10−3s−1 @ 400 ◦C 2.357 nc nc10−3s−1 @ 600 ◦C nc nc nc10−3s−1 @ 800 ◦C nc nc nc10−1s−1 @ 25 ◦C 0.00310 0.0404 0.129101s−1 @ 25 ◦C 0.0729 0.463 1.400103s−1 @ 100 ◦C - 0.256 0.358103s−1 @ 200 ◦C 0.147 0.140 0.0868103s−1 @ 300 ◦C 0.0266 0.0728 0.321103s−1 @ 400 ◦C 0.0412 0.527 0.0540103s−1 @ 600 ◦C 0.0267 0.772 0.276103s−1 @ 800 ◦C 0.733 0.400 0.268103s−1 @ 900 ◦C - nc -103s−1 @ 1000 ◦C 2.94 nc nc

quantities which, in general, are force and displacement.The optimization of the parameters is performed with adedicated algorithm included in the software LS-OPT.

Also for molybdenum, a series of different solutionsare analyzed and the best results, in terms of correlation be-tween experimental and predicted responses, are obtainedwhen the experimental data at different temperatures inquasi-static condition are omitted from the optimizationprocess, as well as the dynamic experimental data attemperature over than 800 ◦C. Each optimization processhas 9 objectives and 5 variables to be determined (C1 is setequal to 0). The target curves are obtained as the averagebehaviour of each loading condition. The optimizedparameters are summarized in Table 2.

For the three materials, the qualitative comparisonbetween experimental and computed quantities is reportedin Fig. 6 for the dynamic tests at high strain-rate. As it ispossible to notice, the optimized Z-A models are able toreproduce the materials behaviours with a good level ofaccuracy.

A more quantitative indication of the error is reportedin Table 3 in terms of percentage Normalized Mean SquareError (NMSE), defined by the relationship:

N M SE =1

n

n∑k=1

(xk − x̂k

max (x)

)2

× 100 (2)

where the index k identifies one of the n points of theobjective (target curve), x represents the experimentaltarget and x̂ represents the computed response.

In Fig. 7 the Z-A models obtained for the threematerials are compared. In Fig. 7a the models arecompared in terms of flow stress curves in quasi-staticloading condition at room temperature. In Fig. 7b, thecomparison is made in terms of equivalent stress as afunction of temperature at 5% of strain. As expected,the models obtained for the two grades of molybdenumproduce very similar results. For these materials, the quasi-static behaviour varying the temperature is extrapolated.

@ 103 s-1

200°C

400°C600°C

800°C

300°Ca)

1000°C

@ 103 s-1

200°C

400°C

600°C

800°C

100°C

300°C

b)

@ 103 s-1

200°C

400°C 600°C

800°C

100°C

300°C

c)

Figure 6. Comparison between experimental and computedquantities: a) for IT180 (analytical optimization); b) and c) forMo1 and Mo2, respectively (numerical inverse optimization).

For what concerns the alloy IT180, the comparison revealsthat the material shows a higher strength with respect tomolybdenum at low temperatures, while the opposite isexpected increasing the temperature, as a consequence ofthe presence of the second low-melting phase.

5. ConclusionsIn this work an experimental test campaign was performedin order to study the strain-rate and temperaturesensitivities of a tungsten alloy (IT180) and pure

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a)@ 25°C, 10-3 s-1

Dynamic

Sta�c

εpl=5%

b)

Figure 7. Comparison between optimized Z-A models obtainedfor the three materials: a) in terms of plastic flow stress in quasi-static loading condition at room temperature; b) in terms ofequivalent stress as a function of temperature in quasi-static anddynamic cases.

molybdenum (in two different grades). The tests wereperformed in tension starting from quasi-static up tohigh strain-rate loading conditions. The dynamic testswere performed using a direct Hopkinson bar setup.The temperature sensitivity was investigated from roomtemperature up to 1000 ◦C both in quasi-static and dynamicregimes. The heating of the specimen was obtained

by an induction coil system controlled in closed loopby means of thermocouples directly welded on thespecimens. The results shown the materials were bothstrain-rate and temperature sensitive. The IT180 wascharacterized by the absence of necking with respect tomolybdenum. All the materials exhibited a decrease ofthe elongation at failure increasing the strain-rate suchthat no reliable results were obtained from dynamic testsat room temperature. The experimental data were usedto extract the coefficients for the Z-A model, used inthe BCC formulation. The parameter identification wasbased on the definition of a multi-objective optimization.Two different approaches were used. In case of IT180an analytical fitting was performed on the true stress vs.true plastic strain. On the other hand, due to instabilityand necking, in case of molybdenum, a numerical inverseapproach was used. The optimized Z-A models were ableto reproduce the materials behaviour with a sufficient levelof accuracy. Comparing the results, it was possible tonotice that the predicted results were in good agreementwith the experimental one. The Z-A models obtained forthe two grades of molybdenum produced very similarresults, while the model obtained for IT180 predicteda higher strength at low temperatures associated to amore significant reduction in strength increasing thetemperature.

References

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